Question

Match the equations with their general solutions. ($n\in I$)

• A. $n\pi +{\tan }^{-1}2$
• B. nπ+(-1)nπ3
• C. 2nπ±2π3
• D. $n\pi -\frac{\pi }{4}$

Answer 1

The expression involving an integer 'n' which gives all solutions of a trigonometric equation is called general solution.

1. tan x = 2

tan x = tan {$ta{n}^{-1}$ (2) }

General solution when tan x = tan α

x = nπ + α

So general solution is x = nπ + $ta{n}^{-1}$ (2) n ∈ I

2. sin x = $\frac{\sqrt{3}}{2}$

sin x = sin $\frac{\pi }{3}$

x = nπ + $(-1{)}^n$ $\frac{\pi }{3}$ n ∈ I

3. cos x = - $\frac{1}{2}$

cos x = cos $\frac{2\pi }{3}$

x = 2nπ ± $\frac{2\pi }{3}$ n ∈ I

4. cot x = -1

cot x = cot(- $\frac{\pi }{4}$)

x = nπ - $\frac{\pi }{4}$ n ∈ I